An accounting period is the time covered by a set of financial statements. Usually you expect to see a 12 month period but there are circumstances where financial statements can be more or less than 12 months for example, if they have started trading or are closing down.
If you have a Limited Company your first accounting period will automatically be the 12 months from the end of the month when your Limited Company was formed and therefore always be slightly longer than 12 months. For example: you form your Company on the 3 June 2017, therefore your first accounting period will be 3 June 2017 to 30 June 2018 and then be the 30 June thereafter. You can choose to change your Limited Company period at any time online but there are rules you need to follow if you wish to do this.
When you are self employed you can choose to keep your accounts for any period you like, but when it comes to completing your self assessment tax return it can be easier to select a period of accounts that matches the tax year (6th April to 5th April each year). The period 1 April to 31 March is commonly used for this reason but it is important to remember that you can choose any accounting period which suits you and you can change it if the need arises.